Singular curves of hyperbolic $(4, 7)$-distributions of type $C_3$

A distribution of rank $4$ on a $7$-dimensional manifold is called a $(4, 7)$-distribution if its local sections generate the whole tangent space by taking Lie brackets once. Singular curves of $(4, 7)$-distributions are studied in this paper. In particular the class of hyperbolic $(4, 7)$-distributions of type $C_3$ is introduced and singular curves are completely described via prolongations for them.